Scretching–Planck Hydrogen-Isotope Coulomb Consistency, Two-Prefactor Relations, and the 1s→2p Excitation

This paper evaluates the Scretching–Planck (SP) coefficient definitions for hydrogen, deuterium, and tritium using the analytic one-electron Coulomb model with physical electron–nucleus reduced masses. Calculations include characteristic radii, contact densities, bound-state energies, excitation photon energies, and the coefficients X₊ and X₋. The analysis verifies the Coulomb virial relations and shows that both the first excitation-energy fraction and X₋/X₊ equal 3/4, while distinguishing their separate mathematical origins. The coefficients are contact-density rescalings, not independently established energy eigenvalues. Without fitting energies, the derivation establishes X± ∝ μ³ and bound-state energies ∝ μ, and distinguishes model predictions from experimentally evaluated ionization energies and nuclear binding.